As with any of the four classes (Alchemist, Chef, Blacksmith or Artisan), you can open your job window/menu. There you find a button called "not learned". If you click on it, you'll see all the crafting recipes that you can get in this game.... including the basic potions.

To get such a recipe, you can visit a "alchemist expert" NPC (located in most towns/cities and marked on the map) and press the button "craft" (not "item list"). If you have the appropriate job level, you can buy the recipes there. Please note, some crafting recipes can't be purchased this way and must be found instead (lvl 40+).

To get the right job level, you need to gather the appropriate materials.

when you find alchemy Expert Npc (in village or Town ), there is 2 button one is ( Item List ) and another ( Craft ) in Craft you find all basic potion, High potion Buff etc.. but you must click name and What lvl its need + how much its cost.